Question

find the value of x.
21
16
x = ?
round to the nearest tenth.

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\), or in terms of finding the hypotenuse \(c = \sqrt{a^{2}+b^{2}}\). Here, \(a = 21\), \(b = 16\), and \(x\) is the hypotenuse.

Step2: Apply the Pythagorean theorem

Substitute \(a = 21\) and \(b = 16\) into the formula \(x=\sqrt{21^{2}+16^{2}}\). First, calculate \(21^{2}=441\) and \(16^{2}=256\). Then, \(21^{2}+16^{2}=441 + 256=697\). So, \(x=\sqrt{697}\).

Step3: Calculate the square root and round

Calculate \(\sqrt{697}\approx26.4\) (rounded to the nearest tenth).

Answer:

\(26.4\)